2011 IEEE Swedish Communication Technologies Workshop (Swe-CTW)
Investigation of Spectrally Efficient Transmission for
Differently Modulated Optical Signals in Mixed Data
Rates WDM Systems
Aleksejs Udalcovs, Vjaceslavs Bobrovs
Institute of Telecommunications
Riga Technical University
Riga, Latvia
Aleksejs.Udalcovs@rtu.lv
networks [6], currently one of the most intensively studied
solutions for raising the system’s total transmission capacity is
improvement of its spectral efficiency (SE) through more
effective use of approximately 60 THz bandwidth offered by
silica optical fibers. In addition, the capacity rise strategy based
on the use of already deployed infrastructure is among the most
cost-effective ones. More efficient use of the channel
bandwidth means that a greater number of informative bits can
be transmitted employing one hertz it, i.e. a smaller number of
channels are required to transmit the same body of data
comparing to the wavelength division multiplexing (WDM)
systems with a low spectral efficiency (<0.2 bit/s/Hz).
Obviously, the SE in WDM systems with traditional
modulation formats (e.g., on-off keying with non-return to zero
encoding (NRZ – OOK)) is much lower as compared with the
systems where advanced modulation formats (together with
additional multiplexing techniques) are employed for optical
signal modulation. The maximum SE which can be obtained
with traditional on-off keying (OOK) modulation formats is ~
0.4 bit/s/Hz [7]. By contrast, in [8, 9, 10] it is reported that the
use of such novel modulation formats as 16 – QAM
(quadrature amplitude modulation) and orthogonal frequencydivision multiplexing (OFDM) together with polarization
division multiplexing (PDM) technique allows achieving SE>6
bit/s/Hz (and even 7 bit/s/Hz). The object of our study is the
minimum allowable channel spacing in combined WDM
systems that can ensure the optical signal detection with
acceptable error probability and the maximum SE of channels.
The offered model of this system can be considered in the
context of next generation optical networks and is intended for
designing the future backbone optical networks. Configuration
of the WDM system was chosen based on evaluation of the
current state of optical networks, the most probable trends in
their development strategy, etc. [11, 12]. In the authors’
opinion and respecting the principle of continuity and
flexibility, the chosen optical signal modulation formats and
per channel bitrates are the most appropriate and fitted for
realization of a combined WDM system at the moment.
Abstract — The authors have studied the possibilities to obtain
the maximum spectral efficiency for a combined wavelength
division multiplexing (WDM) system by minimizing the channel
spacing. The fiber optic transmission systems under study can be
considered in the context of next generation optical networks and
is offered as a model for designing the future backbone networks.
In the case of different telecom operators’ optical networks
merging, in the nearest future the necessity may arise to transmit
variously modulated optical signals over a single optical fiber
(even with different per channel bitrates). In this paper the
authors show an optimal combined WDM system configuration
that provides the least bit-error-rate values for the signals
detected in system’s channels. It is found that the minimal
channel spacing for differently modulated optical signals in the
investigated mixed data rates WDM system is 75 GHz if these
signals are transmitted with 10 Gbit/s and 40 Gbit/s per channel
bitrates. It is revealed that such a system’s average spectral
efficiency depends also on a combined system’s configuration in
the case of channel separation with equal frequency intervals.
Keywords - wavelength division multiplexing (WDM);
modulation formats; spectral efficiency; channel spacing; bit-errorrate.
I.
INTRODUCTION
One of the major problems that will probably intensify
within the next two or five years is capacity shortage in
transmission systems. This trend is due to a rising number of
worldwide internet users and the data volume itself requested
per one user. As a result, the demand for transmission capacity
and information throughout has risen steeply during the last
few years [1, 2]. Besides, the expansion and variety of new
online and broadband services as well as their rapid advance
contribute to this continuous growth in the internet traffic. The
existing transmission systems will be unable to secure
appropriate quality of service (QoS) level and fulfill the service
level agreements (SLA) if the internet traffic keeps doubling
every year as it is now [3, 4]. Currently, to ensure the needed
carrying capacity of a transmission system and the data
throughput of each individual channel the required bandwidth
of backbone fiber optic transmission system (FOTS) networks
is doubled every two years [5].
II.
A. Simulation scheme
In the paper, as a combined FOTS a 9-channel WDM
system is considered in which three different modulation
Since cost reductions and increased flexibility are and will
be the main drivers for the evolution of all optical transport
978-1-4577-1878-6/11/$26.00 ©2011 IEEE
NUMERICAL ANALYSIS AND MODEL
7
formats are used for optical carrier signal modulation. The first
one is the NRZ – OOK, which is a modulation format
traditionally employed in FOTS. The second one is the
orthogonal binary polarization shift keying (2 - POLSK), and
the third – the differential phase shift keying with non-return to
zero encoding (NRZ – DPSK). A similar combined FOTS
model and reasons for selecting these modulation formats have
already been described by the authors in [2]. The system’s
channels are divided into three groups with identical
configuration of the transmitter and receiver as well as
distribution of modulation formats among the channels but
with different central wavelengths of channels. For evaluation
of such a combined system’s performance the quality of optical
signal transmission was analysed only for the central group
channels – i.e. those with number one to three. This was
specially done to take into account linear and nonlinear
crosstalk effects in the optical signal transmission to which the
central group’s channels (from the first to the third system’s
channel) are exposed from the channels of adjacent groups (4th
- 6th and 7th – 9th). As mentioned above, for further analysis of
system’s performance we use channels 1-3, while 4-6 and 7-9
are taken only as sources of interchannel crosstalk (see Fig. 1).
4 – 6 ch Tx
1 – 3 ch Tx
OSA 1
OCombiner
7 – 9 ch Tx
NRZ - Rec
CW
MZM
EBF
The optimal EDFA fixed output power level and the
optimal power level radiated by distributed feedback (DFB)
lasers in the continuous wavelength (CW) mode (which are
used in the channels where NRZ – DPSK modulated optical
signals are transmitted) were reported in [13] to be equal to 4
dBm and 3.5 dBm, respectively. The optimal value of these
parameters ensures the lowest possible average BER of the
detected signals in [1st channel: NRZ – OOK, B = 10 Gbit/s, fc
= 193.075 THz] – [2nd channel: 2 – POLSK, B = 10 Gbit/s, fc =
193.100 THz] – [3rd channel: NRZ – DPSK, B = 10 Gbit/s, fc =
193.125 THz] combined system. For chromatic dispersion
(CD) compensation in the case of 40 Gbit/s per channel bitrates
a dispersion post-compensation module (DCM) is placed at the
other fiber end before the optical power splitter. The used
DCM is based on the chirped fiber Bragg grating (FBG)
technology. This module compensates the CD level
accumulated by a signal during its transmission over the whole
optical fiber length. Then the optical signals are filtered with
Super Gaussian optical filters, converted to electrical signals,
filtered by Bessel electrical filters and, finally, detected.
OSA 2
SSMF 50 km /
NZ – DSF 50 km
OAmplifier
PPG
system model was supplemented with EDFA to take into
account amplified spontaneous emission (ASE) noise assuming
that we are dealing with one sector of an ultra-long haul
backbone optical network. The fiber length was chosen equal
to 50 km in order to avoid a prohibitive growth in the ASE
noise which occurs if the gain of EDFA exceeds 10 dB [2].
1 – 3 ch Rx
Using this simulation scheme and the developed combined
WDM system’s model the minimum allowable channel spacing
and spectral efficiency were found for every system with the
following configuration: [1st: NRZ – OOK (10 or 40 Gbit/s)] –
[2nd: 2 – POLSK (10 or 40 Gbit/s)] – [3rd: NRZ – DPSK (10 or
40 Gbit/s)]. For performance evaluation the eye diagrams of
detected signals and the system’s output optical spectrum were
obtained and further analyzed.
FBG OSplitter
OSGF
ESA
PIN
EBF
BER Est
ES
Q Est
NRZ - OOK
PPG
PDR
OSGF
CW
POLM
ESA
PRx
EBF
BER Est
ES
B. Simulation method and accuracy
This research is based on powerful and widely accepted
mathematical simulation software OptSim 5.2 for solving the
nonlinear Schrödinger equation which describes the optical
signal propagation over a fiber [5]:
Q Est
2 - POLSK
PPG
NRZ - Rec
CW
OPM
EBF
OSGF BDPSK Rx EBF
ESA
BER Est
ES
| |
Q Est
NRZ - DPSK
PPG – Pulse Pattern Generator
CW – Continuous Wavelength
MZM – Mach-Zehnder Modulator
POLM – Polarization Modulator
OPM – Optical Phase Modulator
EBF – Electrical Bessel Filter
OSGF – Optical Super Gaussian Filter
, (1)
where A(t, z) is the optical field; z is the fiber length, [km];
is the linear attenuation coefficient of an optical fiber, [km-1];
is the second-order parameter of chromatic dispersion,
[ps2/nm];
is the third-order parameter of chromatic
dispersion, [ps3/nm]; is a nonlinear coefficient, [W-1.km-1]; t
is the time, [s].
ES - Electrical Splitter
BDPSK Rx – Balanced DPSK Receiver
PRx – POLSK Receiver
PIN – PIN Photodiode
Q Est – Q factor Estimator
BER Est – Bit-Error-Rate Estimator
ESA – Electrical Signal Analyser
Solution for this equation is obtained using time domain
split-step algorithm. The optical signal after propagation over
Δz fiber span will then be described as follows [5, 14]:
Figure 1. Simulation scheme of a developed nine-channel combined WDM
system and block diagram of the channel transmitting and receiving units
for NRZ – OOK, 2 – POLSK and NRZ – DPSK optical signal modulation
formats.
(
Then the NRZ – OOK, 2 – POLSK and NRZ – DPSK
modulated optical signals from transmitters are combined,
optically preamplified by an erbium-doped fiber amplifier
(EDFA) with optimal fixed output power and sent over 50 km
of a standard single mode optical fiber (SSMF, according to
ITU – T Recommendation G.652 D). The combined WDM
)
̂]
[
(
̂[ (
{
̂)
(
)
where ̂ ̂ are linear and nonlinear operators [5, 14]:
8
)]}
(2)
(4)
channel spacing was set for each system. The channel spacing
values were chosen based on the establishment principle of
ITU – T Recommendation G.694.1.
For the performance evaluation two commonly used
references for BER value will be employed. The maximum
permissible BER value for the signals transmitted at 10 Gbit/s
and 40 Gbit/s per channel bitrate is 10-12 and 10-16, respectively
[14]. The BER confidence interval depends on the total number
of simulated bits [14]. As an example, we will assume a 95 %
confidence interval for the BER as a function of the total
number of simulated bits (Ntotal) at a 10-12 nominal (see Fig. 2).
Before analyzing the minimum channel spacing we will
turn to combined WDM systems where optical signals are
transmitted with equal per channel bitrates (only 10 Gbit/s or
40 Gbit/s). Previously it was mentioned that the optimal
configuration of combined WDM system had been developed
based on 10 Gbit/s per channel bitrate. Therefore it is of
importance to find the minimum channel spacing exactly for
this system.
̂
(3)
̂
| |
Figure 2. The 95 % confidence interval for a nominal BER=10-12.
The 95 % confidence intervals for 1024 simulated bits and
nominals of 10-12 and 10-16 (assuming the Gaussian
distribution) are:
[
]
(5)
[
]
(6)
Figure 3. [1st: NRZ – OOK (10 Gbit/s)] – [2nd: 2 – POLSK (10 Gbit/s)] –
[3rd: NRZ – DPSK (10 Gbit/s)] combined system’s output spectrum and
the eye diagrams of detected signals.
As is seen from (5) and (6), the confidence interval for
1024 simulated bits and the nominal of BER = 10-12 is less than
±1 order, while for the nominal of BER = 10-16 it is less than ±2
orders. This evidences that OptSim software allows obtaining
sufficiently accurate preliminary results.
III.
As could be seen from Fig. 3, if for channel separation in
the [1st: NRZ – OOK (10 Gbit/s)] – [2nd: 2 – POLSK (10
Gbit/s)] – [3rd: NRZ – DPSK (10 Gbit/s)] combined system 25
GHz intervals are used, then the system’s channel can easily be
separated one from another using optical filters. As a result,
linear and nonlinear crosstalk influence on the signal
transmission will be negligible. In such a system’s channels the
eye diagrams of detected signals have “eyes” open enough,
with noise and timing jitter influences being insignificant. As a
consequence, the channels’ BER values are sufficiently below
maximum threshold (BER = 10-12, see Fig. 3). In this case the
system’s worst channel is the second one, where 2 – POLSK
modulated signals are transmitted (BER=7.10-19). The channel
spacing reduction to 18.75 GHz leads to the transmission
quality worsening. As is seen in the eye diagrams, the signal
detection with an acceptable error probability is disturbed by
high level noise due to inefficient separation of transmission
channels. This is confirmed by the system’s output optical
spectrum for the 18.75 GHz channel spacing. Indeed, at such
small channel spacing the system’s channels are located so
RESULTS AND DISCUSSION
According to the above mentioned combined WDM system
configuration [1st channel: NRZ – OOK (10, 40 Gbit/s)] – [2nd
channel: 2 – POLSK (10, 40 Gbit/s), 193.100 THz] – [3rd
channel: NRZ – DPSK (10, 40 Gbit/s)], the minimum
allowable channel spacing was studied for all eight possible
mixed data rates of the system. These systems differ from each
other only with per channel bitrates, whereas the distribution of
modulation formats among the channels and the transmitting
and receiving part configuration remain unchanged. The
configuration of each investigated combined system will be
clarified in further discussion of results obtained. The
investigation of the minimum allowable channel spacing was
carried out in order to achieve better utilization of the available
frequency band and larger system channels’ spectral efficiency.
It should be noted that in this research minimum and equal
9
close together that they cannot be filtered even with efficient
wavelength filters. As a result, BER of detected signals for the
first and second system’s channel is larger than the previously
defined threshold. In this case the system’s worst channel is the
first one (NRZ-OOK), where the BER value is larger than 10-9.
Only in the third system’s channel the received optical signals
can be detected with the BER smaller than 10-12.
at 75 GHz (see Fig. 4). This is indicative of significant noise
level and timing jitter of the detected signals.
In further discussion, we will analyze the channel spacing
for 10 and 40 Gbit/s mixed data rate combined WDM systems.
For convenience sake they were divided into two groups. The
first one is combined WDM systems where only in one channel
the optical signals are transmitted at 40 Gbit/s, while in the
remaining two channels the per channel bitrate is 10 Gbit/s.
The second group comprises the systems where in two
channels the optical signals are transmitted at 40 Gbit/s, and
only in one channel – with 10 Gbit/s.
If in all channels of a combined WDM system the optical
signals are transmitted with 40 Gbit/s per channel bitrate, the
minimum channel spacing is 100 GHz, which ensures that the
BER values are lower than the maximum threshold (BER = 1016
, see Fig. 4). In this case the worst system’s channel with
BER = 1.10-14 is the first one (NRZ-OOK). Transmission in
these channels are considerably distorted by adjacent NRZDPSK channels which are the sources of stronger interchannel
crosstalk as compared with the NRZ – OOK or 2 – POLSK
channels (see [13]). The best system’s channel in this case is
the channel where NRZ – DPSK modulated signals are
transmitted with BER = 10-40 (see Fig. 4).
Figure 5. [1st: NRZ – OOK (10 Gbit/s)] – [2nd: 2 – POLSK (10 Gbit/s)] –
[3rd: NRZ – DPSK (40 Gbit/s)] combined system’s output spectrum and
the eye diagrams of detected signals.
It was found that the third system’s configuration: [1st:
NRZ – OOK (10 Gbit/s)] – [2nd: 2 – POLSK (10 Gbit/s)] – [3rd:
NRZ – DPSK (40 Gbit/s)] ensures the detected signal BER
values that are the highest in a system’s channels as compared
with the fourth and the fifth configurations: [1st: NRZ – OOK
(10 Gbit/s)] – [2nd: 2 – POLSK (40 Gbit/s)] – [3rd: NRZ –
DPSK (10 Gbit/s)] and [1st: NRZ – OOK (40 Gbit/s)] – [2nd: 2
– POLSK (10 Gbit/s)] – [3rd: NRZ – DPSK (10 Gbit/s)],
respectively. For these two configurations the detected signal
BER values do not exceed 10-40 for all system channels if 75
GHz channel spacing is used. The third system’s worst channel
is the first one, where the 10 Gbit/s NRZ – OOK modulated
signals are transmitted. At 75 GHz interval it’s BER = 6.10-29
(see Fig. 5).
Figure 4. [1st: NRZ – OOK (40 Gbit/s)] – [2nd: 2 – POLSK (40 Gbit/s)] –
[3rd: NRZ – DPSK (40 Gbit/s)] combined system’s output spectrum and
the eye diagrams of detected signals.
Channel spacing reduction to 75 GHz leads to inefficient
filtering of channels, and, as a result, significant growth in the
BER of detected signals. In this case the best system’s channel
is the third one, since its BER value at a 75 GHz channel
spacing still corresponds to the maximum tolerated, i.e.
BER<10-16 and is not larger than 10-40. Transmission in this
channel degrades only at a 50 GHz channel spacing; as a result,
the third channel “eye” is almost closed and its BER value
(2.10-4) is considerably larger than the previously defined
maximum allowable threshold as compared with the first and
second channel eye diagrams whose eyes almost closes already
If we reduce channel spacing to 50 GHz, the BER values
for the system’s first and second channels still fit maximum
acceptable threshold (BER = 10-12) which was previously
defined for 10 Gbit/s. The highest BER value for these two
channels is for the first one and it is equal to 8.10-13. As for the
10
worst system’s channel at 50 GHz spacing, it is the third one.
Its BER value far exceeds the maximum acceptable error
probability of 10-16 and is equal to 3.10-5. The fourth system’s
worst channel at 50 GHz is the second one, with BER = 4.10-6.
However, the best is the third channel, whose transmission
does not fail even at 25 GHz (in this case BER=8.10-14).
Transmission in the first channel of the 5th system fails at 50
GHz. Its BER for this channel spacing is equal to 1.10-3, and
the eye on the corresponding diagram is completely closed.
However, transmission in the 5th system’s second and third
channel fails only at 25 GHz spacing (BER = 2.10-7 and 2.10-8,
respectively).
value for the NRZ – DPSK channel exceeds the threshold of
BER=10-12 only at 25 GHz interval and it is equal to 5.10-6.
Transmission fails in the 7th system’s first and third channels at
50 GHz spacing, but the second channel’s BER for such
interval is still below 10-16 and equal to 3.10-20. In contrast, the
8th system’s transmission fails in all channels if 50 GHz
intervals are used. The best channel at such spacing is the first
one and its BER is equal to 2.10-12.
In addition, for each configuration of the studied combined
WDM systems the channels’ average spectral efficiency was
calculated. Assuming that we operate with discrete noiseless
channels and all the sent information is received unchanged at
the other end (i.e. BER →0), the system’s average spectral
efficiency (SE, [bit/s/Hz]) can be calculated by the following
formula:
The best configuration of a combined WDM system where
optical signals are transmitted with 40 Gbit/s in two channels is
the sixth one. It provides the lowest average BER value for the
detected signals as compared with the seventh and the eight
configurations: [1st: NRZ – OOK (40 Gbit/s)] – [2nd: 2 –
POLSK (10 Gbit/s)] – [3rd: NRZ – DPSK (40 Gbit/s)] and [1st:
NRZ – OOK (10 Gbit/s)] – [2nd: 2 – POLSK (40 Gbit/s)] – [3rd:
NRZ – DPSK (40 Gbit/s)].
∑
,
(7)
where N is a number of channels in a WDM system, [1]; B is
the bitrate per channel, [10, 40 Gbit/s]; Δf is the channel
spacing, [GHz].
As the result, the following values for spectral efficiency have
been obtained: 0.40 bit/s/Hz for the 1st, 2nd, 3rd, 6th, 7th and 8th
system’s configurations, and 0.27 bit/s/Hz for the 3rd, 4th and 5th
ones.
IV.
CONCLUSIONS
The efficiency of transmission in mixed data rate WDM
systems has been investigated for differently modulated optical
signals. As the model of a developed combined WDM system
meant for the future design of backbone optical networks a
system of the following configuration is offered: [1st channel:
NRZ – OOK (10 or 40 Gbit/s)] – [2nd channel: 2 – POLSK (10
or 40 Gbit/s)] – [3rd channel: NRZ – DPSK (10 or 40 Gbit/s)].
According to this configuration the minimum allowable
channel spacing and the channels average spectral efficiency
for eight different combined systems have been obtained and
analyzed. These systems differ from each other in per channel
bitrates. The minimum channel spacing that ensures the BER
value of detected signals below the maximum threshold of 10-12
for 10 Gbit/s per channel bitrate and 10-16 for 40 Gbit/s is:
Figure 6. [1st: NRZ – OOK (40 Gbit/s)] – [2nd: 2 – POLSK (40 Gbit/s)] –
[3rd: NRZ – DPSK (10 Gbit/s)] combined system’s output spectrum and
the eye diagrams of detected signals.
If for the channel separation a combined 6th configuration
WDM system the 75 GHz intervals are used, the channels’
BER values are not higher than 10-40. As could be seen from
the system’s output optical spectrum, the channels are located
maximally close to each other, so further compaction would
lead to the signal spectrum overlapping as it is shown for 50
GHz spacing (see Fig. 6). In this case the NRZ – OOK and 2 –
POLSK channels are overlapping. As a result, the BER value
for the signals detected in these channels is considerably higher
than 10-16 and is equal to 3.10-3 and 5.10-5, respectively. This

25 GHz if per channel bitrate (B) in each system’s
channel is equal to 10 Gbit/s;

75 GHz if at least in one system’s channel B = 40
Gbit/s;

100 GHz if optical signals are transmitted with 40
Gbit/s per channel bitrate.
Based on these data, the channel’s average spectral
efficiency for each combined system’s configuration has been
estimated. It is equal to:
11

0.27 bit/s/Hz if only in one of the three channels of the
system B = 40 Gbit/s;

0.40 bit/s/Hz if in all system’s channels optical signals
are transmitted with equal per channel bitrate (10 or 40
Gbit/s) or at least in two of the three channels that form
the central group of a system’s channels B = 40 Gbit/s.
An important point is that the channels’ average spectral
efficiency for each combined system’s configuration was
obtained for equal channel spacing. Significantly higher
spectral efficiency could be achieved if for the channel
separation in such mixed data rate WDM systems unequal
intervals were taken.
[6]
[7]
[8]
ACKNOWLEDGMENT
This work has been supported by the European Regional
Development Fund in Latvia within the project Nr.
2010/0270/2DP/2.1.1.1.0/10/APIA/VIAA/002 and by the
European Social Fund within the project „Support for the
implementation of doctoral studies at the Riga Technical
University”.
[9]
[10]
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